The field of the invention is the measurement of dynamic mechanical stress. More particularly, the invention relates to electric and fiber optic systems including stress sensitive transducer elements or combinations of elements which produce a stress dependent electrical or optical signal. In addition to measuring dynamic stress, such systems may be used to measure related variables such as acceleration, vibration, force, strain, stress wave arrival time, and stress wave velocity.
There are many devices currently available for obtaining measurements of dynamic stress. Most of these devices are based on materials which are capable of converting mechanical energy into electrical energy. The mechanical energy represents the elastic energy of compression in response to the applied stress which is to be measured. The electrical energy is then used to produce a stress dependent signal which is processed and transmitted to electronic recording devices.
Two classes of materials are useful for transducing mechanical energy or stress into electrical signals. Once class is the piezoelectric materials which are crystalline substances that develop an electrical polarization proportional to the applied stress. The second class consists of ferroelectric materials which are crystalline substances that can attain a spontaneous and reversible metastable electrical polarization. The electrical response of a ferroelectric substance derives from the stress dependent depolarization of a prepolarized crystal. The electrical response of piezoelectric materials arises from the stress dependent polarization of a nonpolarized crystal.
The response of either class is referred to as the "piezoelectric" response or the "piezoelectric" effect by those who are experienced in the art. Since either type of response is useful in stress transducers, including the present invention, "piezoelectric" effect or response will hereafter refer to the response of either piezoelectric or ferroelectric materials. Furthermore, any reference to "piezoelectric" components will refer to components based on either piezoelectric or ferroelectric materials.
The stress induced changes in electrical polarization produce a change in the electrical potential between at least two opposing faces of properly oriented piezoelectric or polarized ferroelectric crystals. Under conditions in which the two crystal faces are electrically insulated from each other (the open circuit mode), the applied stress can be determined by directly measuring the change in the electrical potential. Under conditions in which the two crystal faces are connected through a small electrical load (the short circuit mode), the applied stress can be determined from the current through the load.
The present invention employs piezoelectric materials in the short circuit mode. For piezoelectric materials the relationship between the electrical polarization and the applied stress can be expressed as: ##EQU1## where P.sub.i are the three components of the polarization vector, o.sub.j are the six components of the stress tensor, and d.sub.ij are the eighteen piezoelectric coefficients relating the i'th and the j'th directions.
A mathematical model for the response of piezoelectric and ferroelectric materials is derived in the Journal of Applied Physics 37(1), 153, (1966) showing the relationship of the electrical current i to the stress induced changes in polarization P: ##EQU2## where A is the electroded area and l is the thickness of the material. Time t is measured from the moment of incidence of a stress wave which propagates through the material with a velocity c. The remaining parameters E.sub.c, P, D, and .beta. reflect the polarization characteristics of ferroelectric materials: ##EQU3## where D is the electric displacement, E.sub.c is a positive reference field magnitude, P.sub.o is the initial remanent polarization, and .eta. is a constant the fixes the polarization nonlinearity. Piezoelectric materials represent the case where (.eta.E.sub.c /P)=1 and .eta.=1. The numerous assumptions and details of this model are discussed in the above reference.
Piezoelectric and ferroelectric stress transducers are typically operated so that the stressed region is in a state of one dimensional strain, and the electric fields produced are along the same dimension as the strain. Such a one dimensional response is experimentally attainable by using specially oriented crystals, e.g. x-out quartz, so that the applied stress is aligned with a high symmetry axis of the crystal. For the one dimensional case equation 1 simplifies to: EQU P(x)=do(x)
The one dimensional response of piezoelectric crystals then simplifies to: ##EQU4## Here, .sigma..sub.0 is the one dimensional stress normal to the front surface electrode, and .sigma..sub.l is the stress at the rear electrode. Equation 5 shows that for time less than the stress wave transit time through the crystal (.sigma..sub.l =0), piezoelectric materials behave as a constant current source from which the current is a linear function of the applied stress. Such optimally oriented piezoelectric crystals are therefore a simple and convenient stress transducer.
Quartz and lithium niobate are examples of piezoelectric materials whose responses are well modelled by equation 5. Quartz has a piezoelectric coefficient of 2.1*10.sup.-8 C/cm.sup.2 kbar and produces a short circuit current output of 0.40 A/cm.sup.2 under an applied stress of 10 kbar over a duration of 0.5 microsecond. This duration corresponds to the stress wave transit time through a 3 mm thick quartz crystal. Lithium niobate has a greater piezoelectric coefficient and produces 1.20 A/cm.sup.2 under a similar 10 kbar stress. FIG. 1 shows a plot of the electrical polarization P for quartz and lithium niobate as a function of pressure.
Quartz has long been a preferred material for stress transducers. Its excellent stability and reproducibility have established quartz as the piezoelectric material of choice despite the availability of many other materials with higher responsivities. Numerous reports in the literature discuss the piezoelectric response of quartz (see for example: J. Appl. Phys. 36(5), 1775 (1965) and Phys. Rev. B 6(12), 4779 (1972). Quartz based stress transducers are commercially available from a number of suppliers.
Ferroelectric materials can have much higher piezoelectric responses and offer the potential of much greater sensitivity in stress transducers. The high responsivity results from the ability of ferroelectric materials to be polarized to remanent polarizations which are much higher than those produced in stressed piezoelectric materials. Consequently, the stress induced depolarization of ferroelectric materials can produce much higher currents than are produced by the stress induced polarization of piezoelectric crystals. For example, the remanent polarizations for three well known ferroelectric materials are given in table 1 below. These values are two to three orders of magnitude higher than the piezoelectric coefficient of quartz. Accordingly, much higher current outputs have been reported for these materials: a 10 kbar stress wave produces 1 A/cm.sup.2 from PVF2 or nearly 300 A/cm.sup.2 from PZT 95/5 compared to 0.40 A/cm.sup.2 from quartz.
TABLE 1 ______________________________________ P .mu.C/cm.sup.2 ______________________________________ Barium titanate 26 Lead zirconium titanate 36 Polyvinylidene difluoride (PVF2) 13 ______________________________________
The drawback to using ferroelectric materials in stress transducers is that the current response is neither constant over time nor linearly dependent on stress. FIG. 2 compares the current outputs of stressed piezoelectric and ferroelectric materials as functions of time. FIG. 2 shows the response given by equation 2 where the output currents have been normalized to the total integrated current (charge). In general, the nonnormalized current response of ferroelectric materials would be much larger than that of piezoelectric materials. FIG. 3 shows the relative depolarization of PVF2 and PZT 95/5 as functions of stress. Ferroelectric materials can serve as useful stress transducers over the range in which the depolarization is a well behaved function of stress. Within this range either the peak current or time integrated current can serve as useful measurements of stress, especially when referenced to a calibrated response curve for the transducer. Commercial ferroelectric based stress transducers are available from a number of sources.
Stress transducers based on the piezoelectric response are generally restricted in applicability by limitations which enter in the processing and transmission of small electrical signals. Successful detection of such signals is limited by the loss in signal strength and the increase in noise which may occur during transmission. The signal to noise ratio is especially noteworthy since transient stress measurements must frequently be made in electronically noisy environments. Examples of such environments include explosive detonations, ballistics experiments, shock waves, combustion, chemical reactors, and heavy industrial machinery.
Some stress transducer designs address the problem of low signal to noise ratio by incorporating an integrated circuit preamplifier in the sensor to condition and amplify the signal for transmission over coaxial cable. The preamplifier complicates the assembly of the sensor. The preamplifier also requires an external power source. In applications requiring signal transmission over distances greater than hundreds of meters, the costs of the cable and repeater amplifiers can become substantial.
To avoid the limitations of electronic signal transmission, several existing and proposed stress transducers produce optical signals that can be transmitted using fiber optic technology. Fiber optic transmission lines are generally less expensive and less susceptible to noise than are the coaxial cables used for electronic signals. U.S. Pat. No. 4,492,121 discloses a method and apparatus for measuring high transient isotropic pressures. The apparatus consists of a fiber optic waveguide having at one end a crystal that fluoresces with a wavelength that varies in response to pressure. U.S. Pat. No. 4,649,528 describes an apparatus for measuring the arrival time and velocity of shockwaves. The apparatus consists of gas filled microballoons mounted on optical fibers. Incident shock waves rapidly compress and heat the gas to produce a short pulse of light. In U.S. Pat. No. 4,581,530 a fiber optic pressure sensor is described in which the pressure is measured by interferometrically observing the deformation of a diaphragm at the end of the fiber.